Block #65,451

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/19/2013, 12:20:37 PM · Difficulty 8.9842 · 6,727,470 confirmations

1CC

Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header

Block Hash

30aa20d9fe449097295614faa13973023cf8aa1ceec1f6cafbee8f92975302eb

View on Chainz ↗

Height

#65,451

Difficulty

8.984153

Transactions

Size

199 B

Version

Bits

08fbf179

Nonce

235

Timestamp

7/19/2013, 12:20:37 PM

Confirmations

6,727,470

Merkle Root

03c01413474eb4107632a7fed750269ce0e3c0d3a68edf2a0dc98e542b3beb6e

Transactions (1)

Coinbase03c01413474eb4…c98e542b3beb6e

1 in → 1 out12.3700 XPM110 B

AGY4TBx7…YfD8h7Va

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.474 × 10⁹¹(92-digit number)

24746825083931884458…40986226162198496879

Discovered Prime Numbers

p_k = 2^k × origin − 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

origin − 1

2.474 × 10⁹¹(92-digit number)

24746825083931884458…40986226162198496879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.949 × 10⁹¹(92-digit number)

49493650167863768916…81972452324396993759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

9.898 × 10⁹¹(92-digit number)

98987300335727537832…63944904648793987519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.979 × 10⁹²(93-digit number)

19797460067145507566…27889809297587975039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.959 × 10⁹²(93-digit number)

39594920134291015133…55779618595175950079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.918 × 10⁹²(93-digit number)

79189840268582030266…11559237190351900159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.583 × 10⁹³(94-digit number)

15837968053716406053…23118474380703800319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.167 × 10⁹³(94-digit number)

31675936107432812106…46236948761407600639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.335 × 10⁹³(94-digit number)

63351872214865624213…92473897522815201279

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer